The function of coefficients of added mass of water

Abstract

The hydrodynamic effect of the water mass of the reservoir on the pressure face of the dam can be determined from the function of the coefficient of the added mass of water obtained in the Westergard solution. For an inclined pressure face, the design standards introduce a correction factor, which is recommended to be taken into account until the slope of the pressure face does not exceed 150; there are no such recommendations for earth dams, however, in the calculations of seismic resistance of earth dams, taking into account hydrodynamic water pressure is also important. Theoretically, the values of the coefficients of the added mass of water can be determined based on the numerical solution of the Laplace equation in the computational domain with given boundary conditions and the graphical-analytical construction of a hydrodynamic grid. Thus, in the MATLAB environment, computational schemes were built for different laying of the pressure head of the dam in the range from vertical to flat with laying 1:3, and orthogonal hydrodynamic grids were built, reflecting the solution of the Laplace equations concerning the functions of pressure and velocity potentials. For all problems, diagrams of the coefficients of the added mass of water are constructed, and they are compared with the Westergaard analytical solution. For practical use in the work, all solutions for constructing diagrams of the coefficients of the added mass of water are presented in the form of a nomogram.